SFM Formulae Booklet

8/12/2019 SFM Formulae Booklet

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S F M n A F M Formulae

P V RamB.Sc., ACA, ACMA

Hyderabad98481 85073

[email protected]


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S F M n A F M Formulae

1. Capital BudgetingTYPES OF CAPITAL BUDGETING PROPOSALSIf more than one proposal is under consideration, then these proposals canbe categorised as follows:

1.Mutually Exclusive Proposals : Two or more proposals are said to beMutually Exclusive Proposals when the acceptance of one proposalimplies the automatic rejection of other proposals, mutually exclusive to it.

2.Complementary Proposals: Two or more proposals are said to beComplementary Proposals when the acceptance of one proposal impliesthe acceptance of other proposal complementary to it, rejection of oneimplies rejection of all complementary proposals.

3.Independent Proposals: Two or more proposals are said to beIndependent Proposals when the acceptance/rejection of one proposaldoes not affect the acceptance / rejection of other proposals.

Present Value (P V) = Annuity (A) / Cost of Capital (K)

O R

Annuity (A) = Present Value (P V) X Cost of Capital (K)

P V of Annuity recd. In Perpetuity = A / R

Where A is Annuity and R is rate of interest.

Discount rate inclusive of inflation is called Money Discount Rate anddiscount rate exclusive of inflation is called Real Discount Rate.

Risk Adj. Disc. Rate (RADR): Risk free rate (R f )+ Risk PremiumO R

Risk Adj. Disc. Rate (RADR): Risk free rate (R f )+ X Risk Premium

Coefficient of Variation =

=


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The lower coefficient of Variation, the better it is.

Profitability Index (P I) =

O R

Profitability Index (P I) =

Accept when P I > 1. The higher the better.

Pay Back Period =Initial Investment

Annual Cash flows

Accept the Project with least Payback Period.

Discounted Payback period is calculated by the same formula as paybackperiod with the exception that discounted cashflows are considered insteadof actual cashflows

= ( + )= Where At is the expected cashflow in period t and Rf is risk free rate of

interest.

Accept when NPV is +ve. The higher the better.

Project NPV is the one which is calculated for the whole Project. Equity NPVis the one which is calculated to know the return of equity holders. In thiscase funds relating to equity holders alone are considered for computation.

I R R is the rate at which the present value cash inflows equal the presentvalue of cash outflows i.e. NPV is zero. For Project IRR all cashflows of theproject are considered and in case of Equity IRR only cashflows relating toequity holders is considered. In case IRR is greater than interest rate onloan, then, the excess rate will accrue to the benefit of equity holders.

Standard Deviation For one year period:

Standard Deviation = Probability X (Given Value - Expected Value) 2


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A Occurs but B does not Occur A Bc = A / B 2. LeasingEvaluation of lease for Lessee: In this case comparison is to be madebetween the NPV of outflows:

a. in case an asset is leased and used, orb. the asset is bought and used.

BELR in case of lessee is the amount at which he will be indifferent betweenbuying an asset and leasing an asset.

Evaluation of lease for Lessor: In this case comparison of P V ofcashflows is to be made between:

a. buying an asset and leasing it getting lease income orb. return expected by investing the funds elsewhere.

BELR for lessor is the amount at which he will be indifferent between buyingthe asset and giving it for lease and / or investing the funds elsewhere andearning desired cost of capital.

Equated yearly Installment = Loan amount / Cumulative AnnuityFactor of desired period

While ascertaining Present Values, people are using different rates fordiscounting like interest rate, net of tax interest rate, cost of capital etc.

based on respective views. Ideal one will be the one using net of taxinterest rate in case of borrowing or using the cost of capital in case of usingown funds.

3. Dividends

Rate of Dividend =Dividend Per Share

Face Value Per ShareX 100

Dividend Yield =Dividend Per Share

Market Price Per Share X 100

Dividend Payout =Dividend Per Share

Earnings Per ShareX 100

Equity dividends are to be paid after paying preference dividends.


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Traditional Theory:

=( + )

= ( + ) Where, P = Mkt. Price of share; D = Dividend per share; R = RetainedEarnings per share; E= EPS & m = a constant multiplier.

Walter Model:

P =+ ( )

Where, P = Mkt. Price of share; D = Dividend per share; r = Return oninternal retentions; E= EPS & k = Cost of Capital.

If r > k, the share price will increase as Div. Payout decreases.

If r = k, then the price will not change with Div. Payout ratio.If r < k, then also share price will increase because Div. Payout increases.

Optimal payout ratio will be for:A growth co. (i.e r > k) is nil.A normal co. (i.e. r = k ) is irrelevant, andA declining (i.e. r < k) firm is 100%

Gordon Model:

=

= ( + )

= (

)

Where, P 0 = Mkt. Price per share before dividend; D 1 = Dividend per sharein year 1; D 0 = Dividend per share in current year; k = cost of equity; g =growth rate of dividends; E = EPS, b = % of earnings retained; and r =Return on internal retentions

g = b * r

In case the dividend amount is fixed for each year, then,

=

If r > k, the share price will increase as Div. Payout decreases.If r = k, then the price will not change with Div. Payout ratio.If r < k, then also share price will increase because Div. Payout increases.


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Optimal payout ratio will be for:A growth co. (i.e r > k) is nil.A normal co. (i.e. r = k ) is irrelevant, andA declining (i.e. r < k) firm is 100%

Modigliani-Miller (M M) Model:If dividend is declared;

=++

= + If dividend is not declared;

=+

= = + Where, P0 = Current Mkt. Price of share; P1 = Mkt. Price at the end ofperiod 1; K= Cost of capital; D1 = Div. In year 1.

Lintner Model:

D 1 = D 0 + [(EPS * Target payout) D 0 ] * Af

D1 = Div. In year 1; D 0 = Div. In year 0; Af = Adj. Factor

Dividend Discount Model:

Intrinsic value = Sum of the PVs of future cash flows.

= PV of dividends + PV of sale value of stock.D 1 + D 2 + D 3 +. . .+ D n + P= (1+k) 1 (1+k) 2 (1+k) 3 (1+k) n (1+k) n

Dn = Dividend of year n; P = Sale price of stock; n = No. Of yrs.;K = Capitalisation rate.

Discount model has 3 sub models:

a. Zero growth model: Each year dividends are fixed:Then, Intrinsic Value = D / K

b.

Constant growth (Gordon Model):Then, Intrinsic Value (P) = D 1 / (K g)

P = Mkt. Price; D 1 = Div. In year 1; K = Cost of capital; g = growthrate of dividends.

c. Variable growth rate model: Usually the three stages of growth,the initial high rate of growth, a transition to slower growth, and


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lastly a sustainable steady growth are considered. For each type ofstage, appropriate variables are considered and PVs are calculatedand sum of the three PVs is the intrinsic value of share.

Holding Period Return: This is the sum of dividend yield and capital gain

yield which is nothing but Total Yield.

Total Yield = + Earning Yield =

4. Capital Markets =

.

The difference between the prevailing price and futures price is known asbasis.

Basis = Spot Price Future Price

In a normal market, spot price will be less than future price as future priceincludes cost of carrying also. Further, apart from carrying cost the futureprice may also change due to dividends etc. So,

Future price = Spot price + carrying cost returns (dividends etc.)

In the case of annual compounding, forward price is calculated by theformula:

A = P (1+r/100) t Where A is the terminal value for an investment of P at r rate of interest perannum for t years. In case interest is compounded n times in a year, then,

A = P (1+r/100n) nt

In case the compounding is more than once on daily basis, then the formulastands modified as:

A = P * e rn Where e is called epsilon, a constant and its value is taken as 2.72

Alternatively,Future Value = Present Value * e rt


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In case any income flows are there, then they are to be deducted and theformula will be:

A = (P I) * e rn Where I is the present value of income inflow.

If the income accretion is in the form % yield y (like in index futures) thenthe formula is:

A = P * e (r-y)n

Options Seller is called Writer or Grantor and the buyer is called simplybuyer or at times as dealer / trader.

An option is said to be in the money when it is advantageous to exercise it.When exercise is not advantageous it is called out of the money .When option holder does not gain or lose it is called at the money .

In case of an option buyer, while there is no limit on the profit he can make,loss is limited to the value of premium he pays to buy the option. Inproblems, if premium is not given, loss is to be taken as zero. It will beopposite in case of option seller i.e. Writer or Grantor.

Intrinsic Value and Time Value of Option: Option premium has twocomponents viz. Intrinsic Value and Time Value. Intrinsic Value is thedifference between Exercise price and Market price or Zero whichever ishigher. Time Value is the excess of Option price over its Intrinsic Value.

European Option can be exercised only on the due date of the option.American Option can be exercised at any time during the period of option.

TIME IS THE ALLY OF WRITER AND ENEMY OF OPTION BUYER SINCE IN THELONG RUN GOOD STOCKS WILL USUALLY DO BETTER.

Black-Scholes Model:

= ( ) ( ), And

= SX + ( +

)

/

= +( )

/= / where,

S = Current Stock Price


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X = Strike Price,r = Continuously Compounded Risk free Interest Ratet = Balance period of option expressed as percentage,N(d 1 ) = Normal distribution of d 1 N(d 2 ) = Normal distribution of d 2

ln = Natural Logarithme = exponential constant with value 2.72,v = Volatility of stock, i.e. Standard DeviationN(d 1 ) is the hedge ratio of stock to options, to keep the writer hedged andN(d 2 ) / ert is Present Value of the borrowing.

The above formula can be used to find the Value of Equity also with littlechanges. In this case, in the place current stock price we need to usecurrent value of business and in the place of strike price we need to usevalue of debt. Rest of all the things are same.

Binomial Model:

Up tick = + = ++

Down tick = + = ++

Where uV t = up value in period t; uV t+1 = uptick value in period t+1 and uV t+2 = uptick value in period t+2 . Similarly, dV t , dV t+1 , & dV t+2.

In case of continuous compounding,Probability = In case of normal compounding,

Probability = + . =

Where e is epsilon (with value 2.72) and t is time period. Please note thatthe t in rt indicates time period whereas the t in u t and d t indicates tick.

Risk neutral Method:Option Value = [C u X P + C d (1-P)] / (1 + r)

Where C u is option value during uptick and C d is option value during downtick P is probability and r is rate of interest.

Put Call Parity Theory: This theory holds good only when exercise priceand maturity of both put and call options are same.


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Floor: Floor means setting the lower limit .Usually the lower limit is set byStrike Price of Put sold.Collar: Combination of Caps and Floor is known as Collars .

Greeks:

Delta is the sensitivity of option price due to change in the value of theunderlying by a unit.Gamma is the sensitivity of option price due to change in Delta.Theta is the sensitivity of option price due to change in expiry date by aday.Rho is the sensitivity of option price due to change in interest rate.Vega is the sensitivity of option price due to volatility of the underlyingasset.

Securities Moving Averages: Moving averages of prices are plotted to make buy selldecisions. Arithmetic Moving Average (AMA) is the simple average of theavailable prices. In case of Exponential Moving Average (EMA) moreweightage is given to current results as against older results. The reductionof weightage is done through a constant known as exponential smoothingconstant or Exponent. EMA is calculated by the formula:

EMA T = aP t + (1 - a) * EMA t-1 = EMA t-1 + a (P t EMA t-1 )

Where, a = Exponent Constant; Pt = Price on respective day and EMAt-1 =Preceding days EMA.

Value of a Bond: Value of a bond is sum of the discounted values of theseries of interest payments (called interest strips) and principal amount(called principal strips) at maturity. Formula is:

V = 1+=1 + 1+ where,In case interest is paid semi annually, formula is:

V =[ ( + )= ] + [

( + )] Where,

V = Value of bond; I = series of interest payments; I/2 = Semi Annualseries of interest payments; F = Face Value incl. Prem., if any; kd =Required. Rate of return; n = maturity period; and 2n = maturity periodexpressed in terms of half yearly periods;


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Bond Value Theorems:

a. When the required rate of return equals the coupon rate, the bond sells atpar value.

b. When the required rate of return exceeds the coupon rate, the bond sells

at a discount. The discount declines as maturity approaches.c. When the required rate of return is less than the coupon rate, the bond

sells at a premium. The premium declines as maturity approaches.d. The longer the maturity of a bond, the greater is its price change with a

given change in the required rate of return.e. Price of a bond varies inversely with yield because as the required yield

increases, the present value of the cash flow decreases; hence the pricedecreases and vice versa.

f. Value of the bond changes with duration. As the bond approaches its

maturity date, the premium / discount will tend to be zero.

Yield is the payment at maturity.

Yield to maturity: The rate of return one earns is called the Yield toMaturity (YTM). The YTM is defined as that value of the discount rate (kd)for which the Intrinsic Value of the Bond equals its Market Price (Note thesimilarity between YTM of a Bond and IRR of a Project). YTM is also knownas COST OF DEBT or REDEMPTION YIELD or IRR or MARKET RATE OFINTEREST or MARKET RATE OF RETURN or OPPORTUNITY COST OF DEBT.

YTM and Bond value have inverse relationship. i.e. if YTM increases Bondvalue will decrease and Vice versa.

Duration of Bond: The term duration has a special meaning in case ofBonds. Duration is the average time taken by an investor to collect hisinvestment. If an investor receives a part of his investment over the time onspecific intervals before maturity, the investment will offer him the durationwhich would be lesser than the maturity of the instrument. Higher thecoupon rate, lesser would be the duration.

Macaulay duration is the weighted average time until cash flows arereceived, and is measured in years.

Modified duration is the percentage change in price for a unit change inyield.


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Macaulay Duration (in years) =[ ( + )= + ( + ) ] / P where,Modified Duration = Macaulay Duration / (1 + YTM / n)

n = number of cash flows; t = time to maturity;C = Cash flows; i = Requd. Yield;M = Maturity Value; P = Bond Price andYTM = Yield to Maturity

(%) =

Modified duration will be always less than Macaulay Duration.

Macaulay duration and modified duration are both termed "duration" and

have the same (or close to the same) numerical value, but it is important tokeep in mind the conceptual distinctions between them. Macaulay duration isa time measure with units in years whereas, Modified duration is a derivative(rate of change) or price sensitivity and measures the percentage rate ofchange of price with respect to yield.

Zero Coupon Bond will have Macaulay Duration equal to maturity period.

Self Amortising Bonds: These are bonds which pay principal over a periodof time rather than on maturity.

Inflation Bonds: These are bonds where coupon rate is adjusted accordingto inflation. That is investor gets inflation free interest. Suppose couponrate is 8% and inflation 6%. Then investor will get 14.48%.

If value of Bond > Market price, then Buy and vice versa.

Bond with variable yield rates: In case a bond has different yields of Y 1 ,Y2 & Y3 in 3 years, then value of bond is calculated by the formula:

=.

( + )+

.

( + )( + )+

.

+ + ( + )

Current Yield is expressed in annualised terms and calculated on marketprice.

Holding period Return = Current Interest Yield + Capital Gain Yield

If Coupon Rate = YTM, then Bond will trade at Par.


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If Coupon Rate > YTM, then Bond will trade at Premium.If Coupon Rate < YTM, then Bond will trade at Discount.(This will be the case when Bond Value = Face Value)

=.

.

Callable Bond is the one where the issuer has an option to call back andretire the bonds before maturity date.

Puttable Bond is the one where the investor has an option to get the Bondredeemed before maturity.

5. Portfolio Management

Variance:Variance Sd 2) = [ = ( )] Where,Xi = Possible returns on security; X = Expected Value of security / Portfolio;

Pi(Xi) = Probability.

Covariance shows the relationship between two variables and is calculatedby the formula;

Cov AB =

(

) where

In case, if in the problem instead of just observations, if probabilities forobservations are also given, then,

Cov AB = ( ) whereRA = Return on security A;R A = Expected or mean return of Security A;RB = Return on security B;R B = Expected or mean return of Security B.

Covariance between two securities may also be calculated by multiplyingrespective betas and the variance of market.

= A B sd m2

Covariance of 2 securities is +ve if the returns consistently move in samedirection.


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Covariance of 2 securities is -ve if the returns consistently move in oppositedirection.Covariance of 2 securities is zero, if their returns are independent of eachother.

The value of covariance will be between - and +

Coefficient of correlation also indicates the relationship between twovariables. It is expressed by the formula:

rAB = = rAB wherer AB = Coefficient of correlation between A & B;CovAB = Covariance between securities A & BSd

A = Standard deviation of security A.

SdB = Standard deviation of security B

Correlation coefficients may range from -1 to 1.A value of +1 indicates a perfect positive correlation between the twosecurities returns and risk will be maximum.A value of -1 indicates perfect negative correlation between the twosecurities return and risk will be minimum; andA value of zero indicates that the returns are independent.

The Variance of a Portfolio consists of 2 components (unlike the return of a

portfolio where weighted average of individual securities is taken):a. Aggregate of the weighted variances of the respective securities andb. Weighted covariances among different pairs of securities.

Calculation of risk In case of only 2 securities, A & B in portfolio, thenVariance of portfolio is given by the formula

Sdp2 = [XA

2 SdA2 + XB

2 SdB2] +2 [XAXB (rAB )]

Sd p 2 = Variance of the portfolio;

XA = Proportion of funds invested in security A;XB = Proportion of funds invested in security B;Sd A2 = Variance of security A;Sd B2 = Variance of security B;SdA = Standard deviation of security A;SdB = Standard deviation of security B, andr AB = Correlation coefficient between the returns of A & B securities.


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In case of perfect +ve correlation, coefficient of correlation, r AB = 1. So, thevariance of portfolio becomes:

Sdp = XA SdA + XB SdB

In case of perfect -ve correlation, coefficient of correlation, r AB = -1. So,the variance of portfolio becomes:

Sdp = XA SdA - XB SdB

In case of perfect no correlation, rAB = 0. So, the variance of portfoliobecomes:

Sdp2 = XA

2 SdA2 + XB

2 SdB2 and

Sdp = [XA2 SdA

2 + XB2 SdB

2]1/2

Calculation of Risk of Portfolio with more than two securities:

Sdp2 = == = == where, Sd p 2 = Variance of Portfolio;

Xi = Proportion of funds invested in security i (the first of a pair ofsecurities).Xj = Proportion of funds invested in security j (the second of a pair ofsecurities).Covij = The Covariance between the pair of securities i and j;

= Correlation Coefficient between securities i and j; = Stabdard deviation of Security i;

= Stabdard deviation of Security j;n = Total number of securities in the portfolio.Calculation of Beta: Covariance Method

= . = = = Where,

r im = coefficient of correlation between scrip i and the market index m;r pm = coefficient of correlation between portfolio p and the market index msd i = standard deviation of returns of stock i;sd m = standard deviation of returns of market index,sd 2 m = the variance of market returns; andsd p = standard deviation of returns of portfolio.

Regression Method : The general form of regression equation is:


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= Where,X = independent variable (market);Y = dependent variable (security), and

,

are constants. Beta is Systematic Risk and Alpha is the intercept on Y

axis.

Beta is calculated by the formula:

= ( ) ( ) ( ) = = ( ) ( ) where,

n = number of items;X = Independent variable (market);Y = Dependent variable (security);

XY = product of dependent and independent variable;X

& Y are respective arithmetic means

Positive beta of security indicates that return on security is dependent onmarket return and will be in the same direction as that of market;Negative beta of security indicates that return on security is dependenton market return and will be in the opposite direction as that of market;Zero beta indicates return on security is independent of market return.

Portfolio beta, = proportion of security beta for security.

Portfolio Beta , p =

=

p = Beta of portfolio;x i = proportion of funds invested in each security; i = Beta of respective securities; andn = number of securities.

Since beta is the relative return of a security vis a vis market return, it canalso be calculated by the formula:

=

Market Beta is taken as one unless otherwise given.

For Risk Free securities like GOI Bonds, T Bills etc. Beta is taken as ZERO (unless otherwise given) implying non existence of Systematic Risk.


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In case of change in capital structure, the company beta will not change butonly the components of debt beta and equity beta will change.

Hedge ratio is computed by the formula:

= Where,

r sf = Correlation Coefficient between spot price and future price;Sd s = Standard Deviation of Changes in Spot Price; andSd f = Standard Deviation of Changes in Future Price.

Formula for Optimum proportion of investment in case of 2 securities i& j is calculated by the formula:

= +

= .+

.

Portfolio Return, r p = = Wherer p = expected return of portfolio;x i = proportion of funds invested in each security;r i = expected return on securities; andn = number of securities.

To calculate return of individual security, following CAPM formula is used:

Ri = + = Rf + (R m Rf ) Where,

Ri = Return of individual security,Rm = Return on market index or Risk PremiumRf = Risk Free rate = Return of the security when market is stationary = Change in return of individual security for unit change in return ofmarket index.Security market line measures the relation between systematic risk andreturn. Formula for Security Line is:

y = x + Where,

x is independent variable and y dependant variable.

Slope of Security line is Beta


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On Return Basis:Expected Return < CAPM Return; Sell, since stock is overvalued.Expected Return > CAPM Return; Buy, since stock is undervaluedExpected Return = CAPM Return; Hold.

On Price Basis:Actual Market Price < CAPM price, stock is undervalued; so BuyActual market Price > CAPM price, stock is overvalued; so, sell.Actual market Price = CAPM price, stock is correctly valued.;

Point of indifference.

Beta in case of Leverage:

= [1 + (1 T) D / E] = + / Where,

l = Leveraged

ul = Unleveraged

D = Debt; E = Equity, and T = Rate of Tax

Equity Beta will be always greater than debt beta as risk of equity holders isgreater than risk of debenture holders.

Risk free securities are Government Securities, T Bills, RBI Bonds etc.

Arbitrage Pricing Theory Model: Uses 4 factors Viz., Inflation and moneysupply, Interest Rate, Industrial Production, and personal consumption.

Under this method, expected return on investment is:

E (R i) = R f + 1 i1 + 2 i2 + 3 i3 + 4 i4 Where,

E(R i) = Expected return on equity;1 , 2 , 3 , 4 are average risk premium (R m R f ) for each of the four factorsin the model and i1 , i2 , i3 , i4 are measures of sensitivity of the particularsecurity i to each of the four factors.

Sharpe Index Model assumes that co-movement between stocks is due tochange or movement in the market index. Return on security i, is calculatedby the formula;

R i = i + i R m + i where,

Ri = expected return on security ii = intercept of the straight line or alpha co-efficient i = slope of straight line or beta co-efficientRm = the rate of return on market index


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i = error term.

According to Sharpe, the return of stock can be divided into 2 components: Return due to market changes (systematic risk)and

Return independent of market changes (unsystematic risk).Total Risk = Systematic risk + Unsystematic Risk

Total variance (Sd i2) = Systematic risk ( i2 X Sd m 2) + Unsystematic risk

Formula for systematic risk is:

Systematic risk = i2 X Variance of market index = i2 X Sd m 2

Unsystematic risk = Total Variance Systematic risk

i.e. Unsystematic risk = Sd i2

- i2

X Sd m2

(Sd m = Standard deviation of Market index; i = Beta of security i; Sd i =Standard deviation of security i)

Portfolio Variance is calculated by the formula:

Sd p 2 = [ ( )= ] + [ ]= Where,Sd p 2 = Variance of portfolio;Xi = Proportion of the Stock in portfolio;

i = Beta of the stock i in portfolio;

Sd m 2 = Variance of the index;USR = Unsystematic Risk.

(Please note the difference between the above formula and the followingformula indicated elsewhere above . Sdp2 = [XA2 SdA2 + XB2 SdB2] +2 [XAXB (rAB )])Coefficient of Determination (r 2 ) gives the percentage of variation in theS ecuritys return that is explained by the variation of the market indexreturn.

Systematic and Unsystematic risk can also be found by the formulas:

Systematic risk = variance of security X r 2 = Sd i2 X r 2

Unsystematic risk = variance of security (1 r 2 ) = Sd i2 (1 r 2 )

Where r 2 = Coefficient of Determination.


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Sharpe and Treynor ratios measure the Risk Premium per unit of Risk fora security or a portfolio of securities for comparing different Securities orPortfolios. Sharpe uses Variance as a measure whereas, Treynor uses Betaas a mesure to compare the Securities or Portfolios.

Sharpe Ratio = (R i R f )/Sd i and

Treynor Ratio = (R i R f )/ i Where,

Ri = Expected return on stock iRf = Return on a risk less assetSd i = Standard Deviation of the rates of return for the ith Security i = Expected change in the rate of return on stock i associated with oneunit change in the market return

The higher the ratio, the better it is.

Jensens Alpha: This is the difference between portfolios return and CAPMreturn.

Jensen Alpha = Portfolio Return CAPM Return.

The higher the Jensen alpha, the better it is.

Sharpes Optimal Portfolio: Steps for finding out the stocks to be includedin the optimal portfolio are as below:

a. Find out the excess return to beta ratio for each stock underconsideration.b. Rank them from the highest to the lowest.c. Calculate C i for all the stocks/portfolios according to the ranked order

using the following formula:

C i = ( )=+ = Where,

= Variance of the index;Ri = Expected return on stock iRf = Return on a risk less asseti = Expected change in the rate of return on stock i associated with

one unit change in the market returnUSR = Unsystematic Risk i.e., variance of stock movement not related

to index movement.


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d. Compute the cut-off point which the highest value of Ci and is taken asC*. The stock whose excess-return to risk ratio is above the cut-offratio are selected and all whose ratios are below are rejected.

e. Calculate the percent to be invested in each security by using thefollowing formula:

% to be invested = = Where,Z i = ( )

Constant Proportion Portfolio Insurance Policy (CPPI) , is a methodwhere the portfolio is frequently reviewed to ensure the investments inshares is maintained as per the following formula:

Investment in shares = m(Portfolio value Floor Value) Floor Value is the value which market expects and m is a constant factor.

When market is raising, more amounts will be invested in Market bywithdrawing from fixed income securities and vice vcersa.

Run Test: If a series of stock price changes are considered, each pricechange is designated + if it represents an increase and if it represents adecrease.

A run occurs when there is no difference between the sign of two changes.When the sign of change differs, the run ends and new run begins.Price Incr. / Decr. +,+,+,-,-,+,-,+,-,-,+,+,+,-,+,+,+,+Run 1 2 3 4 5 6 7 8 9

Run Test is performed as per the following procedure:

First, number of runs r is calculated.Secondly , N+ & N- are calculated. These are the number of +ve & -vesigns in the sample.Thirdly, N is calculated. N = N+ + N- = Total observations 1Fourthly, As per Null hypothesis, the number of runs in a sequence of Nelements as random variable whose conditional distribution is given byobservations of N+ and N- is approximately normal with Mean which iscalculated as

= + +

Fifthly, Standard deviation, is calculated by the formula:


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= ( ) Sixthly, If the sample size is N, then it will have (N - 1) degrees of

freedom. For this particular degrees of freedom, and the given level ofsignificance, using the value t from t-table, Upper and Lower limits arefound by the formula:

Upper / Lower Limit = t * Lastly, If the value of r falls within the upper and lower limits, it is calledweak form of efficiency, and if it falls outside the limits, it is called strongform of efficiency.

Efficient Market Theory is based on the Usage of Available Information byInvestors to optimise their value of Holdings. The 3 forms of Efficiency are:

Weak Form of Efficiency: Market Price is reflected only by historical / pastinformation.

Semi Strong Form of Efficiency: Market Price is reflected by both Pastand Public information.

Strong Form of Efficiency: Market Price is reflected by Past , Public as wellas Private Information .

6. Mutual Funds Net Assets of the Scheme is calculated as below:

Market value of investments + Receivables + Accrued Income + Other Assets Accrued Expenses Payables Other Liabilities

Valuation Rules are:Nature of Asset Valuation Rule

Liquid Assets e.g. cash held As per books.All listed and traded securities (otherthan those held as not for sale) Closing Market Price

Debentures and Bonds Closing traded price or yield

Unlisted shares or debentures

Last available price or book valuewhichever is lower. Estimated MarketPrice approach to be adopted ifsuitable benchmark is available.

Fixed Income Securities Current Yield.

The asset values as obtained above are to be adjusted as follows:Additions DeductionsDividends and Interest accrued Expenses accruedOther receivables considered good Liabilities towards unpaid assets


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Other assets (owned assets) Other short term or long term liabilities

N A V = Net Assets of the scheme / Number of Units Outstanding

Expense ratio = Expense / Avg. Value of Portfolio O R

Expense per unit / Avg. Net Value of Assets

=[( @ ) ( @ . . )]( @ . . )

7. Money Markets Effective Yield (EY) is Calculated by the formula,

=

Where,

FV = Face Value, SV = Sale Value

If discount is collected upfront, discount is calculated by the formula:

= . . .

Effective Discount (ED)

=

8. Forex Direct quote is the one where the home currency is quoted per unit offoreign currency (eg. USD 1 = INR 60) and vice versa is the indirect quote i.e where the foreign currency is quoted per unit of home currency (eg. INR1 = USD 0.01667).

=

PIP is the smallest movement a price can make.

Bid rate is Buy rate and Ask rate is Sell rate.

Spread is the difference between Bid and Ask.


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American Terms are the rates quoted in USD per unit of foreigncurrency .

European Terms are the rates quoted in foreign currency per unit of USD.

In a Direct Quote Premium / Discount is calculated by the formula:

Premium / Discount = [Forward (F) Spot (S)] / Spot (S) X (12 / n) X 100

In an Indirect Quote it is calculated by the formula:

Premium / Discount = [Spot (S) Forward (F)] / Forward (F) X (12 / n) X 100

Where n is number of months.

Interest Parity Equation:

1 + r d = (F / S) * (1 + r f ) where,

r d = Domestic rate of interest, F = one unit of foreign currency, S = Spotrate and r f = foreign rate of interest.

In case a Forward Contract is to be extended, then existing contract is to becancelled and new contract is to be entered.Similarly, in case of early delivery also, original contract is to be cancelledand settlement of currency being delivered at spot rate.

9. Merger & Acquisitions Combined Value = Value of Acquirer + Value of Target co. + Value of Synergy Cost of Acquisition.

In case cashflows grow at a constant rate after forecast period, TerminalValue (T V) is:

= + In case cashflows are fixed every year, =

Where,

F C F = Free Cashflow; k = Cost of Capital and g = growth rate.

Depending on the availability of information, Terminal Value can also becalculated by the formulae:


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P V RamB.Sc., ACA, ACMA

Hyderabad98481 85073

[email protected]

Documents

SFM Formulae Booklet